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Finding an approximation of the inverse of the covariance matrix, also known as precision matrix, of a random vector with empirical data is widely discussed in finance and engineering. In data-driven problems, empirical data may be ``contaminated''. This raises the question as to whether the approximate precision matrix is reliable from a statistical point of view. In this paper, we concentrate on a much-noticed sparse estimator of the precision matrix and investigate the issue from the perspective of distributional stability. Specifically, we derive an explicit local Lipschitz bound for the distance between the distributions of the sparse estimator under two different distributions (regarded as the true data distribution and the distribution of ``contaminated'' data). The distance is measured by the Kantorovich metric on the set of all probability measures on a matrix space. We also present analogous results for the standard estimators of the covariance matrix and its eigenvalues. Furthermore, we discuss two applications and conduct some numerical experiments.

We present subwavelength resonant lattices fashioned as nano- and microstructured films as a basis for a host of device concepts. Whereas the canonical physical properties are fully embodied in a one-dimensional periodic lattice, the final device constructs are often patterned in two-dimensionally-modulated films in which case we may refer to them as photonic crystal slabs, metamaterials, or metasurfaces. These surfaces can support lateral modes and localized field signatures with propagative and evanescent diffraction channels critically controlling the response. The governing principle of guided-mode, or lattice, resonance enables diverse spectral expressions such that a single-layer component can behave as a sensor, reflector, filter, or polarizer. This structural sparsity contrasts strongly with the venerable field of multi-layer thin-film optics that is basis for most optical components on the market today. The lattice resonance effect can be exploited in all major spectral regions with appropriate low-loss materials and fabrication resources. In this paper, we highlight resonant device technology and present our work on design, fabrication, and characterization of optical elements operating in the near-IR, mid-IR, and long-wave IR spectral regions. Examples of fabricated and tested devices include biological sensors, high-contrast-ratio polarizers, narrow-band notch filters, and wideband high reflectors., Comment: 11 pages, 10 figures

We introduce a novel neural volumetric pose feature, termed PoseMap, designed to enhance camera localization by encapsulating the information between images and the associated camera poses. Our framework leverages an Absolute Pose Regression (APR) architecture, together with an augmented NeRF module. This integration not only facilitates the generation of novel views to enrich the training dataset but also enables the learning of effective pose features. Additionally, we extend our architecture for self-supervised online alignment, allowing our method to be used and fine-tuned for unlabelled images within a unified framework. Experiments demonstrate that our method achieves 14.28% and 20.51% performance gain on average in indoor and outdoor benchmark scenes, outperforming existing APR methods with state-of-the-art accuracy., Comment: Accepted at ECCV 2024. Project page: https://gujiaqivadin.github.io/posemap/

Magnetic skyrmions offer promising prospects for constructing future energy-efficient and high-density information technology, leading to extensive explorations of new skyrmionic materials recently. The topological Hall effect has been widely adopted as a distinctive marker of skyrmion emergence. Alternately, here we propose a novel signature of skyrmion state by quantitatively investigating the magnetoresistance (MR) induced by skyrmionic bubbles in CeMn2Ge2. An intriguing finding was revealed: the anomalous MR measured at different temperatures can be normalized into a single curve, regardless of sample thickness. This behavior can be accurately reproduced by the recent chiral spin textures MR model. Further analysis of the MR anomaly allowed us to quantitatively examine the effective magnetic fields of various scattering channels. Remarkably, the analyses, combined with the Lorentz transmission electronic microscopy results, indicate that the in-plane scattering channel with triplet exchange interactions predominantly governs the magnetotransport in the Bloch-type skyrmionic bubble state. Our results not only provide insights into the quantum correction on MR induced by skyrmionic bubble phase, but also present an electrical probing method for studying chiral spin texture formation, evolution and their topological properties, which opens up exciting possibilities for identifying new skyrmionic materials and advancing the methodology for studying chiral spin textures., Comment: 17 pages,5 figures,submitted

Recovering high quality surfaces from noisy point clouds, known as point cloud denoising, is a fundamental yet challenging problem in geometry processing. Most of the existing methods either directly denoise the noisy input or filter raw normals followed by updating point positions. Motivated by the essential interplay between point cloud denoising and normal filtering, we revisit point cloud denoising from a multitask perspective, and propose an end-to-end network, named PCDNF, to denoise point clouds via joint normal filtering. In particular, we introduce an auxiliary normal filtering task to help the overall network remove noise more effectively while preserving geometric features more accurately. In addition to the overall architecture, our network has two novel modules. On one hand, to improve noise removal performance, we design a shape-aware selector to construct the latent tangent space representation of the specific point by comprehensively considering the learned point and normal features and geometry priors. On the other hand, point features are more suitable for describing geometric details, and normal features are more conducive for representing geometric structures (e.g., sharp edges and corners). Combining point and normal features allows us to overcome their weaknesses. Thus, we design a feature refinement module to fuse point and normal features for better recovering geometric information. Extensive evaluations, comparisons, and ablation studies demonstrate that the proposed method outperforms state-of-the-arts for both point cloud denoising and normal filtering.

Fully supervised log anomaly detection methods suffer the heavy burden of annotating massive unlabeled log data. Recently, many semi-supervised methods have been proposed to reduce annotation costs with the help of parsed templates. However, these methods consider each keyword independently, which disregards the correlation between keywords and the contextual relationships among log sequences. In this paper, we propose a novel weakly supervised log anomaly detection framework, named LogLG, to explore the semantic connections among keywords from sequences. Specifically, we design an end-to-end iterative process, where the keywords of unlabeled logs are first extracted to construct a log-event graph. Then, we build a subgraph annotator to generate pseudo labels for unlabeled log sequences. To ameliorate the annotation quality, we adopt a self-supervised task to pre-train a subgraph annotator. After that, a detection model is trained with the generated pseudo labels. Conditioned on the classification results, we re-extract the keywords from the log sequences and update the log-event graph for the next iteration. Experiments on five benchmarks validate the effectiveness of LogLG for detecting anomalies on unlabeled log data and demonstrate that LogLG, as the state-of-the-art weakly supervised method, achieves significant performance improvements compared to existing methods., Comment: 12 pages